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Reliable estimation of the MRI-visible effective axon radius using light microscopy: the need for large field-of-views

Laurin Mordhorst¹, Maria Morozova^2,3, Sebastian Papazoglou¹, Björn Fricke¹, Jan Malte Oeschger¹, Henriette Rusch³, Carsten Jäger², Markus Morawski^2,3, Nikolaus Weiskopf^2,4, and Siawoosh Mohammadi^1,2
¹Institute of Systems Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg, Germany, ²Department of Neurophysics, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ³Paul Flechsig Institute of Brain Research, University of Leipzig, Leipzig, Germany, ⁴Felix Bloch Institute for Solid State Physics, Faculty of Physics and Earth Sciences, Leipzig, Germany

Synopsis

MRI-based models enable non-invasive characterization of brain microstructure, e.g. the effective axon radius ($$$r_{\text{eff}}$$$). Often, these models were validated by small-field-of-view microscopy (sFoVM) images (~10³ axons). As $$$r_{\text{eff}}$$$ is dominated by large, sparsely occurring axons, sFoVM-based estimations may miss large axons and underestimate $$$r_{\text{eff}}$$$. We employed an in-house developed pipeline to estimate $$$r_{\text{eff}}$$$ on large-scale light microscopy (lsLM) sections with similar spatial extent as the voxel sizes in human MRI systems. Taking lsLM as a baseline, we showed that sFoVM is an unsuitable reference for $$$r_{\text{eff}}$$$ and verified the potential of $$$r_{\text{eff}}$$$ to capture relevant spatial, anatomical variation.

Introduction

The assessment of microstructural properties through MRI-based models in white matter tissue of the human brain, such as the MRI-visible effective radius ($$$r_{\text{eff}}$$$) ¹, is of increasing interest, but requires thorough validation studies and has been questioned as being a meaningful neuroimaging biomarker ². However, the literature is currently lacking a reliable reference for the validation of $$$r_{\text{eff}}$$$. As $$$r_{\text{eff}}$$$ is weighted towards the tail of the axon radii distribution, it is necessary to representatively capture large, sparsely occurring axons and therefore validate MRI-based models at similar scale i.e. the spatial extent of typical MRI voxels (~1 mm³). Often, the validation of $$$r_{\text{eff}}$$$ was done based on small-field-of-view microscopy (sFoVM) images covering a few thousand axons or less ^1,3-6, e.g. obtained from manually labeled electron microscopy (mlEM) sections ^3-6. While sophisticated electron microscopy (EM) techniques have been demonstrated to provide high resolution images at the desired scale ⁷, we instead employed CNN-based (convolutional neural network), automated segmentation on large-scale light microscopy (lsLM) sections. Albeit suffering from variations in contrast and being incapable to resolve very small axons, lsLM may prove to be a cost- and time-efficient approach to generate reference data at the required spatial extent (>= 1mm²). Using lsLM-based estimation as a reference method, we assessed the error in sFoVM-based estimations of $$$r_{\text{eff}}$$$. Moreover, we investigated the potential of $$$r_{\text{eff}}$$$ to capture anatomical variation of the pool of large axons across a human corpus callosum sample to verify its general potential as a meaningful neuroimaging biomarker.

Materials and Methods

Dataset
A human corpus callosum sample (see Figure 1) was obtained at autopsy with prior informed consent (male, 74 years, 24 hours postmortem delay) and approval by the responsible authorities (Approval \#205/17‐ek). We acquired lsLM images of 18 semi-thin (500 nm) sections using a Zeiss AxioScan Z1 (pixel size: 0.1112 µm). The spatial extent ranged from 0.3 mm² to 9.2 mm² (on average: 3.5 mm²). For six lsLM sections, consecutively cut, ultra-thin (50 nm) EM sections were acquired using a Zeiss EM 912 Omega (pixel size: 0.0043 µm) and subsections (size: 0.005 mm² to 0.014 mm²; on average: 0.007 mm²) were manually segmented as axon, myelin or background to obtain mlEM images.

Effective axon radius estimation
Individual axon radii ($$$r$$$) were obtained from lsLM sections and mlEM subsections using an in-house developed pipeline (see Figure 2) ⁸. The effective axon radius was computed as $$$r_{\text{eff}} = \sqrt[4]{<r^6>/<r^2>}$$$ ¹ .

Experiment 1: Influence of FoV on $$$r_{\text{eff}}$$$
To assess the influence of the FoV on the estimation accuracy of $$$r_{\text{eff}}$$$, we sampled the distribution of $$$r_{\text{eff}}$$$ over randomly positioned lsLM subsections and compared it to $$$r_{\text{eff}}$$$ obtained from the corresponding whole lsLM sections and consecutively cut mlEM subsections. This procedure was repeated for varying FoV (0.002 mm² to 0.64 mm² but at most 10 % of the whole section area) and the number of subsections per FoV was chosen so that the accumulated subsection areas matched approximately 25 times the area of the whole lsLM section. To evaluate the typical error for a FoV that resembled the average size of the mlEM subsections (0.007 mm²), we determined the error ¹ as the range of relative errors of the median with respect to the corresponding whole section $$$r_{\text{eff}}$$$ for a FoV of 0.005 mm².

Experiment 2: Relationship between large axons and $$$r_{\text{eff}}$$$
We computed a linear regression to predict the fraction of large axons ($$$f_{\text{large}}$$$) from $$$r_{\text{eff}}$$$ over all lsLM sections. The threshold for large axons ($$$r >= 1.6$$$ µm) was determined so that $$$r_{\text{eff}}$$$ was halved when axons with radii above this threshold were removed.

Results

Experiment 1: Influence of FoV on $$$r_{\text{eff}}$$$
$$$r_{\text{eff}}$$$ obtained from small-FoV subsections as well as the estimation of $$$r_{\text{eff}}$$$ from mlEM consistently underestimated $$$r_{\text{eff}}$$$ (see Figure 3). With increasing FoV, both underestimation of the median and spread of the subsampled $$$r_{\text{eff}}$$$ decreased. Errors of the median $$$r_{\text{eff}}$$$ ranged from -22.6 % to -12.3 % for a FoV of 0.005 mm² that resembled the mlEM FoV used in this study.

Experiment 2: Relationship between large axons and $$$r_{\text{eff}}$$$
The fraction of large axons $$$f_{\text{large}}$$$ was linearly related to $$$r_{\text{eff}}$$$ ($$$f_{\text{large}}$$$ [%] = -3.14 [%] + 2.85 * [1/µm] * $$$r_{\text{eff}}$$$ [µm], R² = 0.88) (see Figure 4).

Discussion

We demonstrated that the estimation of $$$r_{\text{eff}}$$$ from sFoVM is an unsuitable method to generate a robust reference for $$$r_{\text{eff}}$$$ due to underestimation (-22.6 % to -12.3 %), likely because large, sparsely occurring axons are underrepresented. The linear relationship between the fraction of large axons and $$$r_{\text{eff}}$$$ indicated that at the spatial extent of typical MRI voxels (~ 1 mm³), $$$r_{\text{eff}}$$$ scaled with the ensemble of large axons ($$$r >= 1.6$$$ µm) rather than being dominated by individual, very large axons in the investigated corpus callosum sample. Further studies are being conducted to confirm these observations by assessment of the accuracy of the suggested automated segmentation from lsLM and to relate $$$r_{\text{eff}}$$$ to the underlying axon radii distribution in a more meaningful way than the employed histogram split.

Conclusion

A robust reference for $$$r_{\text{eff}}$$$ requires a large ensemble of axons at MRI-similar scale and therefore large field of view microscopy combined with an automated approach.

Acknowledgements

The Max Planck Institute for Human Cognitive and Brain Sciences has an institutional research agreement with Siemens Healthcare. NW was a speaker at an event organized by Siemens Healthcare and was reimbursed for the travel expenses.

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n° 616905.

This work was supported by the German Research Foundation (DFG Priority Program 2041 "Computational Connectomics”, [MO 2397/5-1; MO 2249/3–1], by the Emmy Noether Stipend: MO 2397/4-1) and by the BMBF (01EW1711A and B) in the framework of ERA-NET NEURON and the Forschungszentrums Medizintechnik Hamburg (fmthh; grant 01fmthh2017).

References

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Figures

Figure 1: Schematic of the human corpus callosum sample. LsLM sections (red and blue) were acquired for 18 regions. Additionally, consecutively cut EM sections (red) were acquired and manually labeled for the following regions: anterior genu (G1, G2), posterior genu (PG2), midbody (M3), isthmus (I2) and splenium (S3).

Figure 2: The axon radius estimation pipeline ⁸. Axon instances (b)) were identified through connected-component labeling after pixel-wise semantic segmentation (a)) ⁹. Subsequently, axon radii were approximated as radii of circles with equivalent areas (c)). Semantic segmentation was skipped for mlEM images.

Figure 3: Influence of the FoV on $$$r_{\text{eff}}$$$. For six regions of the corpus callosum, box plots (horizontal lines in boxes denote median values; boxes include central 50 % of the values; whiskers include central 95 % of the values) of $$$r_{\text{eff}}$$$ for random lsLM subsections (black) are shown for varying FoV. The corresponding $$$r_{\text{eff}}$$$ of the whole lsLM sections (blue) and their consecutively cut mlEM subsections (red) are marked. The number of axons ranged from 1.0*10³ to 1.7*10³ in mlEM and 3.2*10⁵ to 1.3*10⁶ in lsLM.

Figure 4: Relationship between $$$r_{\text{eff}}$$$ and the fraction of large axons. Point markers denote estimations of $$$r_{\text{eff}}$$$ from large-scale light microscopy (lsLM) sections of a human corpus callosum. The linear regression line ($$$f_{\text{large}}$$$ [%] = -3.14 [%] + 2.85 * [1/µm] * $$$r_{\text{eff}}$$$ [µm], R² = 0.88) is plotted as a dashed line. The number of identified axons per region ranged from 2.5*10⁴ to 1.3*10⁶ (on average: 4*10⁵).

Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)

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